Optimal oscillation-center transformations
type: Item
instance of: scholarly article
title: Optimal oscillation-center transformations
zbMATH Open document ID: 0595.70013
DOI: 10.1016/0167-2789(85)90132-0
author: R. L. Dewar
published in: Physica D
publication date: 1985-01-01T00:00:00Z
full work available at URL: metadc1212907
review text: The author considers Hamiltonian systems with the Hamiltonian of the form \(H_ 0(p)+H_ 1(q,p,t)\) and defines an ''optimization'' criterion for canonical transformations, continuously connected with identity, such that new P and Q are to be as close as possible (in a suitable sense) to traditional action-angle or oscillation-center variables. A variational principle is proposed, which is based on minimization of mean square generalized force over phase space and time. The optimal oscillation- center transformation for physical pendulum is constructed analytically. A modified principle for relativistic systems is presented in an Appendix.
Mathematics Subject Classification ID: 70H15
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 70G10
Mathematics Subject Classification ID: 70E05
zbMATH DE Number: 3958790
zbMATH Keywords: decay of Fourier spectrum
zbMATH Keywords: primary KAM-surfaces
zbMATH Keywords: orbit topology
zbMATH Keywords: integrable systems
zbMATH Keywords: Galilean invariance
zbMATH Keywords: ''optimization'' criterion
zbMATH Keywords: action-angle
zbMATH Keywords: oscillation-center variables
zbMATH Keywords: variational principle
zbMATH Keywords: minimization of mean square generalized force
zbMATH Keywords: optimal oscillation-center transformation
zbMATH Keywords: physical pendulum
reviewed by: Yuri E. Gliklikh
MaRDI profile type: Publication
OpenAlex ID: W2038946267
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description: scientific article; zbMATH DE number 3958790